<s>
In	O
mathematics	O
,	O
a	O
linear	B-Architecture
operator	I-Architecture
is	O
called	O
locally	O
finite	O
if	O
the	O
space	O
is	O
the	O
union	O
of	O
a	O
family	O
of	O
finite-dimensional	O
-invariant	O
subspaces	O
.	O
</s>
<s>
Every	O
linear	B-Architecture
operator	I-Architecture
on	O
a	O
finite-dimensional	O
space	O
is	O
trivially	O
locally	O
finite	O
.	O
</s>
<s>
Every	O
diagonalizable	B-Algorithm
(	O
i.e.	O
</s>
<s>
there	O
exists	O
a	O
basis	O
of	O
whose	O
elements	O
are	O
all	O
eigenvectors	O
of	O
)	O
linear	B-Architecture
operator	I-Architecture
is	O
locally	O
finite	O
,	O
because	O
it	O
is	O
the	O
union	O
of	O
subspaces	O
spanned	O
by	O
finitely	O
many	O
eigenvectors	O
of	O
.	O
</s>
